Best Known (60−21, 60, s)-Nets in Base 32
(60−21, 60, 363)-Net over F32 — Constructive and digital
Digital (39, 60, 363)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 3, 33)-net over F32 (see above)
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 7, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 10, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 21, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
(60−21, 60, 1639)-Net in Base 32 — Constructive
(39, 60, 1639)-net in base 32, using
- net defined by OOA [i] based on OOA(3260, 1639, S32, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3260, 16391, S32, 21), using
- 1 times code embedding in larger space [i] based on OA(3259, 16390, S32, 21), using
- discarding parts of the base [i] based on linear OA(12842, 16390, F128, 21) (dual of [16390, 16348, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- discarding parts of the base [i] based on linear OA(12842, 16390, F128, 21) (dual of [16390, 16348, 22]-code), using
- 1 times code embedding in larger space [i] based on OA(3259, 16390, S32, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3260, 16391, S32, 21), using
(60−21, 60, 8788)-Net over F32 — Digital
Digital (39, 60, 8788)-net over F32, using
(60−21, 60, large)-Net in Base 32 — Upper bound on s
There is no (39, 60, large)-net in base 32, because
- 19 times m-reduction [i] would yield (39, 41, large)-net in base 32, but